被动约束层阻尼梁动力学优化研究

研究被动约束层阻尼(passive constrained layer damping,PCLD)梁的动力学优化问题,优化变量为PCLD的起始位置、覆盖长度、阻尼层厚度和约束层厚度。在局部覆盖PCLD梁动力学特性的传递函数解的基础上,建立PCLD梁的单目标和多目标优化模型。单目标优化中以结构模态损耗因子最大为优化目标,讨论约束条件中PCLD附加结构质量系数对优化结果的影响。多目标优化中以各阶模态损耗因子最大、各阶固有频率改变量最小和PCLD附加的结构质量最小为优化目标,增加约束层纵振频率的约束条件,讨论优化目标函数中各权重系数对优化结果的影响。此外,还在有限元软件MSC.Patran/Nastran中二次开发出PCLD梁动力学优化模块。两种方法的优化结果一致,验证本文计算结果的正确性。     

A compressional-shear model for vibration control of beams with active constrained layer damping

In the modeling of the active constrained layer damping (ACLD) structures, the transverse displacements of the constraining layer and the host structures are usually assumed to be compatible. However, when performing active control, even a small difference between the transverse displacement of the constraining layer attached with actuator and that of the host structures bonded with sensor may destabilize the closed-loop control system. In order to understand the effect of incompatible transverse displacements, a model for the beam with ACLD in which both compressional vibration and shear damping are considered, is developed. In this model, the viscoelastic layer is modeled to carry not only the shear strain but also the peel strain. In addition, a thorough solution scheme to obtain the eigenvalues and frequency response of the closed-loop controlled beam is also given based on multiple shooting method. The effects of the compressional vibration on passive and active control are investigated through simulation examples. It is found that the compressional vibration can significantly affect the frequencies and damping ratios of higher-order modes of an actively controlled beam and may even destabilize the active control.     

DYNAMIC BOUNDARY CONTROL OF BEAMS USING ACTIVE CONSTRAINED LAYER DAMPING

A globally stable boundary control strategy is developed to damp the vibration of beams fully treated with active constrained layer damping (ACLD) treatments. The devised boundary controller is compatible with the operating nature of the ACLD treatments where the strain induced generates a control force and moment acting at the boundary of the treated beam. The development of the boundary control strategy is based on a distributed-parameter model of the beam/ACLD system in order to avoid the classical spillover problems resulting from using ‘truncated’ finite element models. Such an approach makes the boundary controller capable of controlling all the modes of vibration of the ACLD-treated beams and guarantees that the total energy norm of the system is decreasing continuously with time. The control strategy is provided also with a dynamic compensator to shape the vibration damping characteristics of the ACLD in the frequency domain. The effectiveness of the ACLD in damping out the vibration of cantilevered beams is determined for different control gains and compared with the performance of conventional passive constrained layer damping (PCLD). The results obtained demonstrate the high damping characteristics of the boundary controller particularly over broad frequency bands.     

子结构界面连接参数识别的波传播法

提出一种基于波传播法识别子结构连接界面刚度和阻尼的新方法。以子结构在平面内的弯曲振动为例,将单元的状态变量与波模式联系起来。通过单元波幅系数的识别,得到连接界面的位移和力向量,再由结点上位移连续及力平衡条件,求得连接界面各个自由度上的动刚度。在识别过程中,将动刚度分离为实部和虚部,以便于连接刚度和阻尼的独立识别。为了提高识别精度,选择一定的频率范围,在每一频率下求得连接界面的刚度和阻尼,最后求出统计平均值作为界面的连接参数。数值仿真算例表明本方法具有良好的识别精度和数值稳定性,是一种极有潜力的参数辨识方法。     

Modeling and analysis of rotating plates by using self-sensing active constrained layer damping

This paper proposes a new finite element model for active constrained layer damped (CLD) rotating plate with self-sensing technique. Constrained layer damping can effectively reduce the vibration in rotating structures. Unfortunately, most existing research models the rotating structures as beams that are not the case many times. It is meaningful to model the rotating part as plates because of improvements on both the accuracy and the versatility. At the same time, existing research shows that the active constrained layer damping provides a more effective vibration control approach than the passive constrained layer damping. Thus, in this work, a single layer finite element is adopted to model a three-layer active constrained layer damped rotating plate. Unlike previous ones, this finite element model treats all three layers as having the both shear and extension strains, so all types of damping are taken into account. Also, the constraining layer is made of piezoelectric material to work as both the self-sensing sensor and actuator. Then, a proportional control strategy is implemented to effectively control the displacement of the tip end of the rotating plate. Additionally, a parametric study is conducted to explore the impact of some design parameters on structure??s modal characteristics.     

Vibration analysis of a beam with partially distributed internal viscous damping

In this paper, governing equations of vibration for a beam with distributed internal viscous damping are established by using Timoshenko beam theory and Hamilton's principle. Then, the transfer matrix method is applied to obtain the frequency equations for the beam. The results reveal, when the internal viscous damping fully distributes along the beam, that the natural frequency decreases with the increasing damping and drops to a zero value at a certain critical damping. While the damping is locally distributed, damped frequency, mode shape and transient response time are affected most significantly by locating the damped segment at the position with maximum bending moment. The flexural amplitudes and phase angles of a beam excited by the resonant harmonic load can be effectively predominated by tuning the damping value.     

局部粘弹性被动约束阻尼梁的振动分析

针对夹层约束阻尼梁结构的减振特性进行深入研究.应用粘弹性材料的耗能原理结合模态应变能法对局部粘弹性被动约束阻尼简支梁的振动特性进行数值分析,对梁铺设阻尼层前后的时域和频域特性分别进行比较,可以得出约束阻尼梁的振动得到有效抑制,同时看到模态应变能法对板梁结构的分析更便捷.     

Vibration suppression of atomic-force microscopy cantilevers covered by a piezoelectric layer with tensile force

In this paper, vibration suppression of a micro-beam covered by a piezoelectric layer is studied. The micro-beam is modeled with the specific attention to its application in AFM. The AFM micro-beam is a cantilever one which is stimulated close to its natural frequency by applying a harmonic voltage to the piezoelectric layer. The beam is an Euler-Bernoulli beam which abbeys Kelvin-Voigt model. Using such model supplies the comparison between elastic and viscoelastic beams; and one of the most important properties of viscoelastic materials, damping effect can readily be investigated. The pump provides an axial load with the result that it suppresses the vibrations. First, the vibration equations are extracted using Lagrangian and extended Hamiltonian method in vertical, longitudinal, as well as torsional directions and are discretized by exploiting the Galerkin mode summation approach. The discretized time-domain equations are solved by the aid of the Runge-Kutta method. The viscoelastic beam is compared with the elastic one, and the effects of damping ratio on vibration responses are presented. Additionally, the effects of micro-pump load, excitation voltage, and initial twist angle are investigated on the amplitude of vibration and natural frequency of system. It is observed that viscoelasticity of beam and axial load of the pump reduce vibrations and provide uniform time-domain responses without beatings.     

切割对磁约束阻尼处理固支板的振动特性的影响

在约束层根部设置引力排列的磁体,阻尼层的剪应变将大于传统约束阻尼处理(passive constrained layer damping treatment, PCLD)的剪应变,因此,采用磁约束阻尼处理(magnetic constrained layer damping treatment, MCLD)可使系统的阻尼得到显著地改善.文中应用假设模态法研究工程中常见的两边固支约束阻尼板的磁约束处理减振效果, 推导出由板的横向模态坐标表示的特征方程.通过考察固支板的第一阶扭转模态(m=1,n=1)的损耗因子,研究将阻尼层等分切割为总的尺寸不变的两块阻尼层的阻尼变化情况.分析表明,在覆盖面积相同时,将阻尼块沿x方向等分为2块,将每块放置在板的宽度方向的边部,并沿模态节线y=W/2对称,可使MCLD获得更好的阻尼改进效果.     

Frequency-dependent damping model for the hydroacoustic finite element analysis of fluid-filled pipes with diameter changes

The integration of a model for longitudinal hydroacoustic fluid damping in thin hydraulic pipes in 3D finite element models is presented in this paper. In order to perform quantitative prediction of the vibroacoustic behavior and resulting noise levels of such fluid-structure coupled system due to hydraulic excitation, an accurate frequency-dependent fluid damping model including friction effects near the pipe wall is required. This step is achieved by matching complex wave numbers from analytical derivation into a parameterized damped wave equation and consecutive translation into finite element modeling.Since the friction effect close to the pipe wall changes locally with the inner pipe radius, the fluid damping model is applied segment-wise in order to model the influence of cross-sectional discontinuity, such as orifices, on the oscillating pressure pulsations. A component synthesis approach, which uses pipe segments as substructures, allows a simple model generation and fast computation times.The numerical harmonic results are compared to experimental frequency response functions, which are performed on a hydraulic test bench driven by a dynamic pressure source in the kHz-range.     

含弹性约束复合阻尼板的振动机理与特性

为了实现对磁致伸缩和压电材料迟滞特性的描述,建立高精度前馈补偿系统,对Preisach模型一阶回转曲线的预测方法进行了研究。首先,介绍了一阶回转曲线及经典插法预测一阶回转曲线的基本原理,着重指出线性经典插值法对Preisach模型一阶回转曲线的预测存在不足;其次,在此基础上,利用非线性变换的思想,提出了辅助线法预测一阶回转曲线;最后,实验比较了超磁致伸缩材料（giant magnetostrictive material,简称GMM）与压电陶瓷（piezoelectric ceramic transducer,简称PZT）两种迟滞情况下,辅助线法和经典插值法对迟滞一阶回转曲线的预测结果。实验结果表明：在GMM迟滞下,对任意一阶回转曲线的预测数据,辅助线法的均方根误差（root mean square error,简称RMSE）最大减少为经典插值法的14.22％;对所有预测数据,辅助线法的RMSE减少为经典插值法的29.42％;在PZT迟滞下,对任意一阶回转曲线的预测数据,辅助线法的RMSE最大减少为经典插值法的18.18％;对所有预测数据,辅助线法的RMSE减少为经典插值法的41.07％。辅助线法对一阶回转曲线的预测精度整体高于经典插值法,且迟滞效应的非线性误差越高,预测精度较经典插值法越优异。     

含弹性约束复合阻尼板的振动机理与特性

针对汽车车身减振降噪需求,开发新型复合黏弹性阻尼材料。基于经典的自由阻尼和约束阻尼耗能原理,提出了一种含弹性约束的具有剪切和弯曲复合耗能机制的复合阻尼层结构。基于层间位移连续关系和薄板理论建立了阻尼复合板的位移方程和应变能能量方程,针对局部阻尼敷设及四边简支边界条件,结合假设模态法,推导出了复合阻尼板的运动微分方程、振动频率特征值方程等,求解得到了复合阻尼板的固有频率及损耗因子。复合阻尼层可用于研究单相材料不同参数特性及多相材料性能对比,且随着弹性层的上移,减振性能越好。复合耗能机理公式的推导,也为其在汽车上应用提供理论依据。     

约束层阻尼梁厚度变形的实验研究

约束层阻尼是减振降噪的一种有效方法,Mead-Markus模型不能解释约束层阻尼梁中黏弹层的相对厚度变形.为解释这种变形,Miles和Reinhall提出TD (thickness deformation)模型.文中通过实验的方法验证TD模型的有效性, 并对这种相对变形进行分析讨论.实验结果显示,相对于Mead-Markus模型,尽管TD模型可能不是一种精确的理想模型,但它适用于更宽的激励频率,并可提高模型的分析精度.     

Finite element model updating of vibrating structures under free-free boundary conditions for modal damping prediction

A method to predict resonance frequencies and modal loss factors of bare and damped samples, using constrained layer damping treatment, under free-free boundary conditions is proposed. In a first phase, measurements of the frequency response functions of these two specimens are performed. In a second phase, a finite element model of the undamped sample is developed. The novelty lies in the consistent modelling of the suspension with spring-damper elements defined with stiffness and damping coefficients with fixed values over the whole considered frequency range. By updating these, the agreement between experiments and simulation is further improved. In a third phase, a finite element model of the damped sample, with constrained layer damping material, is realized. A good agreement with experimental results is obtained thanks to an optimization algorithm used to determine the material parameters of the viscoelastic layer at various frequency. A comparison with experimental results, from a Dynamic Mechanical Analysis, confirms the consistency of the results from the optimization process.     

主动约束层阻尼板的振动控制研究

研究局部附加主动约束层阻尼（active constrained layer damping,ACLD）结构板的振动控制问题。基于Hamilton原理，提出一种新的建立主动约束导板动力学模型的方法，同时给出一种用于确定粘弹材料GHM（Golla-Hughes-Mctavish）模型参数的优化问题。采用GHM方法描述弹性材料的本构关系，将粘弹性材料的动力特性描述与工程上最常用的有限元分析结合起来，推导得到ACLD结构的动力学方程为标准二阶定常线性系统方程。应用LQR控制理论进行结构振动控制仿真，结果表明，本文给出的新建模方法是准确可靠的，ACLD结构能够有效抑制结构振动。     

Prediction of vibration of rotating damped beams with arbitrary pretwist

A solution procedure for the bending–bending vibration of a rotating damped beam with arbitrary pretwist and an elastically restrained root is derived. The viscous damping is assumed to be proportional to the distributed mass. The general complex system is divided into two subsystems. The physical meanings of the subsystems are studied. The exact complex frequency relations between two viscously damped beams with arbitrary pretwist and elastic root are revealed. The underdamping, critical damping and overdamping systems are analyzed. Moreover, the influence of the parameters on the decay rate, the natural frequencies, the critical damping, and the phenomenon of divergence instability are investigated.     

电流变液夹层梁滑模振动控制的研究

采用Rayleigh-Ritz方法推导电流变夹层梁的动力学方程，在夹层梁动力分析的基础上，基于滑模控制理论，设计电流变夹层梁的主动控制的控制器。研究确定性系统和不确定性系统控制率生成。数值仿真的结果表明这些控制策略是十分有效的和现实可行的。     

Research on the design of non-traditional dynamic vibration absorber for damped structures under ground motion

An analytical approach is presented to investigate the optimal problem of non-traditional type of Dynamic vibration absorber (DVA) for damped primary structures subjected to ground motion. Different from the standard configuration, the non-traditional DVA contains a linear viscous damper connecting the absorber mass directly to the ground instead of the main mass. There have been many studies on the design of the non-traditional DVA for undamped primary structures. Those studies have shown that the non-traditional DVA produces better performance than the standard DVA does. When damping is present at the primary system, there are very few works on the non-traditional dynamic vibration absorber. To the best of our knowledge, there is no study on the design of non-traditional DVA for damped structures under ground motion. We propose a simple method to determine the approximate analytical solutions of the nontraditional DVA when the damped primary structure is subjected to ground motion. The main idea of the study is based on the criterion of the equivalent linearization method to replace approximately the original damped structure by an equivalent undamped one. Then the approximate analytical solution of the DVA’s parameters is given by using known results for the undamped structure obtained. Comparisons have been done to validate the effectiveness of the obtained results.     

桥梁结构损伤的振动模态检测

首先介绍了桥梁结构损伤检测的振动模态方法的原理及其４ 个要素。总结了用模态参数（固有频率、阻尼比及位移振型）进行损伤检测评估的困难,进而阐述应变模态测量的原理及其用于桥梁结构损伤检测时,相对于位移模态的优势。由于应变模态方法应用于实桥检测受到传统应变测量手段的制约,本文最后提出了一种通过相邻点振动位移的测量,推估桥梁在动载作用下的应力状态,进行实桥损伤检测的途径,并推荐一种新型低频高灵敏度传感器作为位移测量用传感器。     

某机载电子设备振动模态与频响分析

首先从模态振型叠加的角度分析了正弦激励下具有比例阻尼的系统输出位移响应,讨论了一般粘滞阻尼时系统用复模态参数表示的频率响应函数。对给定的工程算例,运用MSC.Patran和Nastran软件进行电子设备的模态分析、扫频振动以及随机振动的频响分析和数值仿真。最后基于模态叠加理论分析了系统的冲击响应问题,并计算了简化模型在给定冲击条件下的位移响应。